Data & Graphs

Depth · one concept from first principles · step 2 of 4

Change the total and every share changes

A circle graph gives the shares of marbles by color, and one color's count is known. After that color is given away, we need what percent of the rest is red.
Share of marbles by color Red (40%) Blue (30%) Yellow Purple (10%)
Data & probabilityRatios
Your answer
How to solve
Strategy Work Backwards — Percentages are useless until we know what they are percentages of, so turn the graph into counts first. Then remove the yellow marbles and work the percent out again -- against the new, smaller total.
1STEP 1

Find the yellow share

The four slices fill the whole circle, so their percentages add to 100.

100 - 40 - 30 - 10 = 20
2STEP 2

Turn a share back into the total

The 10 yellow marbles are that 20%, so 10 is one fifth of all the marbles.

10 ÷ 20 × 100 = 50
3STEP 3

Count the red marbles

Red is 40% of those 50 marbles.

50 × 0.4 = 20
4STEP 4

Take the yellow ones away and re-divide

Giving away 10 marbles leaves 40, and the red ones are untouched, so divide 20 by the new total.

50 - 10 = 40, 20 ÷ 40 = 0.5
Answer
50%
Count it out: 20 red, 15 blue and 5 purple make 40 marbles, and 20 of those 40 are red.
Takeaway

A share can change without the count changing -- when the total shrinks, every remaining share grows.

  • Find the yellow share
  • Turn a share back into the total
  • Count the red marbles
  • Take the yellow ones away and re-divide
Where next?
Another one like thissuggested
12 practice problems
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